A110685 Expansion of (1+4*x-2*x^2-4*x^3+4*x^4) / ((x-1)*(3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1)).

-1, 2, 0, -13, 60, -220, 765, -2662, 9384, -33457, 120048, -431896, 1554957, -5598250, 20151564, -72527377, 261011940, -939300196, 3380216661, -12164232958, 43774972368, -157531648801, 566904871752, -2040106024480, 7341678056925

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-6,-10,-3,8,6,6).

Formula

a(n) = -6*a(n-1) - 10*a(n-2) - 3*a(n-3) + 8*a(n-4) + 6*a(n-5) + 6*a(n-6) for n>5. - Colin Barker, May 19 2019

G.f.: (1+4 x-2 x^2-4 x^3+4 x^4)/(-1-6 x-10 x^2-3 x^3+8 x^4+6 x^5+6 x^6) - Harvey P. Dale, Jun 02 2024

Maple

seriestolist(series((1+4*x-2*x^2-4*x^3+4*x^4)/((x-1)*(3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1)), x=0, 25)); -or- Floretion Algebra Multiplication Program, FAMP Code: tessum(infty)-4basejforsumseq[ + 'i - .25'j + .25'k - .25j' + .25k' - .5'ii' - .25'ij' - .25'ik' - .25'ji' - .25'ki' - .5e], Sumtype is set to: sum[Y[15]] = sum[ * ], Fortype is set to: 1A.

Mathematica

CoefficientList[Series[(1 + 4*x - 2*x^2 - 4*x^3 + 4*x^4)/((x - 1)*(3*x^2 + 3*x + 1)*(2*x^3 + 2*x^2 + 4*x + 1)), {x, 0, 50}], x] (* G. C. Greubel, Sep 06 217 *)
LinearRecurrence[{-6, -10, -3, 8, 6, 6}, {-1, 2, 0, -13, 60, -220}, 30] (* Harvey P. Dale, Jun 02 2024 *)

Prog

(PARI) Vec((1+4*x-2*x^2-4*x^3+4*x^4)/((x-1)*(3*x^2+3*x+1)*(2*x^3+2*x^2+4*x+1))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Cf. A110683, A110684, A110686.

Sequence in context: A274107 A122688 A293936 * A225480 A286118 A286084

Adjacent sequences: A110682 A110683 A110684 * A110686 A110687 A110688

Keyword

sign,easy

Author

Creighton Dement, Aug 02 2005

Status

approved